We know that the alternating group of degree $n>7$ has an irreducible character of degree $n-1$. The latter number is the smallest nontrivial one for each the alternating group has an irreducible character of that degree.

Does the Alternating group of degree $n>7$ has exactly one irreducible character of degree $n-1$?

We know that the alternating group of degree $n>7$ has an irreducible character of degree $n-1$. The latter number is the smallest nontrivial one for each the alternating group has an irreducible character of that degree.

Does the Alternating group of degree $n>7$ have exactly one irreducible character of degree $n-1$?